What is the integral of 8*2^{-x}-2 ?

The integral of 8*2^{-x}-2 is -(2^{-x+3})/(ln(2))-2x+C

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integral of 8*2^{-x}-2

\int 8 \cdot 2^{- x} - 2 d x

- \frac{2 ^{- x + 3}}{ln ( 2 )} - 2 x + C

Solution steps

\int 8 \cdot 2^{- x} - 2 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 8 \cdot 2^{- x} d x - \int 2 d x

\int 8 \cdot 2^{- x} d x = - \frac{2 ^{- x + 3}}{ln ( 2 )}

\int 2 d x = 2 x

= - \frac{2 ^{- x + 3}}{ln ( 2 )} - 2 x

Add a constant to the solution

= - \frac{2 ^{- x + 3}}{ln ( 2 )} - 2 x + C

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What is the integral of 8*2^{-x}-2 ?
The integral of 8*2^{-x}-2 is -(2^{-x+3})/(ln(2))-2x+C